Multicointegration and Present Value Relations

It is well-known that if the forcing variable of a present value (PV) model is an integrated process, then the model will give rise to a particular cointegrating restriction. In this paper we demonstrate that if the PV relation is exact, such that no additive error term appears in the specification, then the variables will be multicointegrated such that the cumulation of cointegration errors at one level of cointegration will cointegrate with the forcing variable. Multicointegration thus delivers a statistical property of the data that is necessary, though not sufficient, for this class of models to be valid. Estimation and inference of the model are discussed and it is shown that provided the PV relation is exact the discount factor of the model can be estimated with a rate of convergence that is faster than the usual super-consistent rate characterizing estimators in the cointegration literature. Finally, the paper is completed with two empirical analyses of PV models using term structure data and farmland data, respectively